Singular Linear-Quadratic Zero-Sum Differential Games and H∞ Control Problems

Valery Y. Glizer received his Ph.D. in mathematics and physics in 1980. From 2007-2020, he served as an Associate/Full Professor at the Department of Mathematics in the ORT Braude College of Engineering, Karmiel, Israel. Currently, Prof. Glizer serves as a researcher at The Galilee Research Center for Applied Mathematics, ORT Braude College of Engineering, Karmiel, Israel. His main areas of research are dynamic games, optimal control, robust control, singular perturbations, systems theory and time delay systems.Oleg Kelis received his M.Sc. in mathematics (with highest honors) in 2008 and his Ph.D. in 2019. Currently Dr. Kelis serves as an adjunct lecturer at the Department of Mathematics, Ort Braude College of Engineering, Karmiel, Israel, and at the Faculty of Mathematics, Technion-Israel Institute of Technology, Haifa, Israel. His fields of research are differential games, optimal control, singularly perturbed problems.

“The book seems to be well structured and comprehensible, in that each chapter contains the same approach to the analysis … type of games, so that readability is guaranteed … . each chapter contains a section including some concluding remarks and a related literature review. The introduction of the book is quite short and basically presents the history of the class of games to be treated, together with a rich overview of the recent contributions in the applied mathematics literature.” (Arsen Palestini, Mathematical Reviews, May, 2023)“The present book formulates the theoretical analysis of the singular games and provides academic and real life examples which illustrate the theoretical results and their applicability. This book is of great interest and importance for researchers working in applied mathematics, control theory, mechanical engineering and biology.” (Savin Treanta, zbMATH 1504.49001, 2023)

• Introduction.- Examples of Singular Extremal Problems and Some Basic Notions.- Preliminaries.- Singular Finite-Horizon Zero-Sum Differential Game.- Singular Infinite-Horizon Zero-Sum Differential Game.- Singular Finite-Horizon $H_{\inf}$ Problem.- Singular Infinite-Horizon $H_{\inf}$ Problem.